SPECIAL RELATIVITY BASICS Flashcards
postulates of SR
laws of physics are invariant
speed of light is constant
time dilation formula
delta t = gamma * proper time
proper time
the shortest time possible between 2 events
what frame does proper time occur in?
the frame in which A and B occur in the same location
length dilation
proper length = L * gamma
proper length
largest length possible
what frame is proper length measured in
frame where events happen at the same time
lorentz invariants
(delta s )^2
c
when to use lorentz transformation
when we know the space time coordinates in one frame and want to find them in the other
space time interval
(delta s)^2 = (c delta t)^2 - (delta x)^2 - (delta y)^2 - (delta z)^2
spacelike events
travels more in space than time
shallower line
space time interval squared < 0
timelike
travels more in time than space
steeper line
space time interval squared > 0
light like
travels at c
y = x
spacetime interval = 0
events in the undefined region of a light cone
to get to these, you would have to travel faster than c
they can be observed as we wait for the light to travel to us
causally linked
negative spacetime interval
lots of time but little space between events
velocity addition fromula
uā = u - v / 1 - uv/c^2
experimental evidence supporting SR
- due to time dilation, muons will have a longer lifetime if they are moving
- in particle accelerators, particles also have a lifetime that increases with speed
- doppler effect
what is conserved in frames throughout SR
energy and momentum
invariants VS conserved quantities
invariants have the same value throughout all reference frames eg c and (mc^2)^2 and delta s squared
some quantities are conserved in all frames, but have different values in different frames
eg E and p
energy equation
E^2 - (pc)^2 = (mc^2)^2
total energy squared - pc squared = rest energy squared
inelastic collisions
E and p are conserved
total energy = gamma mc^2 = EK + mc^2
momentum = gamma m u
photons
photons have no mass
light like as they travel at c
spacetime interval squared = 0
(c delta t)^2 = (delta x)^2
total energy squared - (pc)^2 = 0
E = pc
